Файл:Lissajous curve 5by4.svg

A Lissajous curve, that can be expressed in parametric form as:

[math]\displaystyle{ \lt semantics\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mstyle displaystyle="true" scriptlevel="0"\gt \lt mi\gt x\lt /mi\gt \lt mo\gt =\lt /mo\gt \lt mi\gt A\lt /mi\gt \lt mi\gt sin\lt /mi\gt \lt mo\gt ⁡\lt !-- ⁡ --\gt \lt /mo\gt \lt mo stretchy="false"\gt (\lt /mo\gt \lt mi\gt a\lt /mi\gt \lt mi\gt t\lt /mi\gt \lt mo\gt +\lt /mo\gt \lt mi\gt δ\lt !-- δ --\gt \lt /mi\gt \lt mo stretchy="false"\gt )\lt /mo\gt \lt mo\gt ,\lt /mo\gt \lt mspace width="1em"\gt \lt /mspace\gt \lt mi\gt y\lt /mi\gt \lt mo\gt =\lt /mo\gt \lt mi\gt B\lt /mi\gt \lt mi\gt sin\lt /mi\gt \lt mo\gt ⁡\lt !-- ⁡ --\gt \lt /mo\gt \lt mo stretchy="false"\gt (\lt /mo\gt \lt mi\gt b\lt /mi\gt \lt mi\gt t\lt /mi\gt \lt mo stretchy="false"\gt )\lt /mo\gt \lt /mstyle\gt \lt /mrow\gt \lt annotation encoding="application/x-tex"\gt {\displaystyle x=A\sin(at+\delta ),\quad y=B\sin(bt)}\lt /annotation\gt \lt /semantics\gt }[/math]<img alt="{\displaystyle x=A\sin(at+\delta ),\quad y=B\sin(bt)}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b9efe37aae3e167657e1b0c03bedb58b5cf7e57" style="vertical-align: -0.838ex; width:33.445ex; height:2.843ex;"/>

with [math]\displaystyle{ \lt semantics\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mstyle displaystyle="true" scriptlevel="0"\gt \lt mi\gt a\lt /mi\gt \lt mo\gt =\lt /mo\gt \lt mn\gt 5\lt /mn\gt \lt /mstyle\gt \lt /mrow\gt \lt annotation encoding="application/x-tex"\gt {\displaystyle a=5}\lt /annotation\gt \lt /semantics\gt }[/math]<img alt="{\displaystyle a=5}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8af5051af2d25f1eb8431da126b102533f224d1a" style="vertical-align: -0.338ex; width:5.491ex; height:2.176ex;"/>, [math]\displaystyle{ \lt semantics\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mstyle displaystyle="true" scriptlevel="0"\gt \lt mi\gt b\lt /mi\gt \lt mo\gt =\lt /mo\gt \lt mn\gt 4\lt /mn\gt \lt /mstyle\gt \lt /mrow\gt \lt annotation encoding="application/x-tex"\gt {\displaystyle b=4}\lt /annotation\gt \lt /semantics\gt }[/math]<img alt="{\displaystyle b=4}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d63e1be76f1c81e4d7d9b4355ba9a715dbd4ca3" style="vertical-align: -0.338ex; width:5.258ex; height:2.176ex;"/> and [math]\displaystyle{ \lt semantics\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mstyle displaystyle="true" scriptlevel="0"\gt \lt mi\gt δ\lt !-- δ --\gt \lt /mi\gt \lt mo\gt =\lt /mo\gt \lt mi\gt π\lt !-- π --\gt \lt /mi\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mo\gt /\lt /mo\gt \lt /mrow\gt \lt mn\gt 2\lt /mn\gt \lt /mstyle\gt \lt /mrow\gt \lt annotation encoding="application/x-tex"\gt {\displaystyle \delta =\pi /2}\lt /annotation\gt \lt /semantics\gt }[/math]<img alt="{\displaystyle \delta =\pi /2}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d58cf73c22f3b86529a7f0234780ae2cf03a363" style="vertical-align: -0.838ex; width:7.804ex; height:2.843ex;"/>. I created it with the following GNUplot code:

set samples 5000
set terminal svg
set output "Lissajous_curve_5by4.svg"
# plotting within a square
set size square
# remove most of information from the picture
set noxtic
set noytic
set key off
# plot
set parametric
a=5
b=4
delta=pi/2
plot [0:2*pi] sin(a*t + delta),sin(b*t) with lines linewidth 2

and then I post-processed with Inkscape